What have you seen that leads you to believe this is actually going to happen?
The data suggests it will happen. Women, minorities, and young people are all voting hard against the GOP - they will never win another national election without it being handed to them by the Democrats unless the platform changes. Either the GOP organization believes falsely that Obama is the reason (in which case they will lose in 2016 before waking up), or they realize that the platform is not sustainable moving forward.
I believe evangelicals have a lot of pull in the GOP, but I do not believe the GOP is made up entirely of evangelicals. It's mostly driven by rich people who want to stay rich and get richer. If all they care about is money, then they will push every social aspect of the platform to wherever the money is best.
How would 'the GOP' go about doing this?
Marginalize the Tea Party. Have major party figureheads and Fox News come out and decry the lack of teamwork. Christie scored huge points in both voter bases doing this during the NJ storm. It works because voters are tired of a shitty government, and when some strong-spoken person in authority comes along and tries to whip politicians into action, it connects with red and blue voters.
At the same time, re-frame arguments. The government shouldn't be allowed to tell us we can't smoke MJ if we don't want to; regulate it and make a shit-ton of money. Fix the economy and we can move illegals into citizenship and jobs instead of deporting them. Shift religious talks away from Christianity as a persecuted religion, and towards the spirit/letter of the First Amendment. None of those framed properly would incite any great outcry from Republican voters, especially when they turned on the TV to see Bill O'Reilly agreeing with them.
Local Congressional and Senatorial candidates sure as fuck aren't going to give up a winning formula.
True. When they campaign in the Bible Belt, they will still be batshit conservative. But in order to suck the teat, you have to support the candidate, and they will support a moderate Jeb Bush over Hillary Clinton any day - because they end their own careers to do anything else. They can pick their favorites in the primaries sure, but by and large money and fame and face time wins there and the national GOP has the money, the celebrities, and the cable network.
Is this just a blue-sky theory of yours, or what?
It's logical. The GOP is a business masquerading as a house of religion, and that is no longer a profitable business model.